Certain practical applications of data processing systems relate to fitting models to sets of data. For example, in applications such as speech processing, signal processing, econometric data prediction, demographic analysis and the like, a set of data points are first collected from a real world process. It is desired then to find a set of mathematical equations which can be used to model the process accurately, for example, to predict the future behavior of the real-world system.
Determining the number of dimensional constraints on the collected data, or equivalently the topological dimension, dT, is an important problem in the study of nonlinear system responses. For example, three-coordinate data may fill a volume, lie on a surface, be confined to a curve, or even degenerate to a point, reflecting zero, one, two, or three independent constraints (representing a topological dimension, dT, of three, two, one, or zero, respectively). In the case of a real-world system in which linear responses may be assumed, this problem is able to be robustly solved by matrix decomposition techniques such as Singular Value Decomposition (SVD) or eigenvalue decomposition. These modeling methods assume that linear functions will adequately fit the data. However, such linear techniques cannot generally be directly applied to an instance of a nonlinear system with satisfactory results.